Density Evolution (DE) analysis has been applied to characterize the asymptotic performance of message passing-based decoding on graphs for low density parity check codes [1]} and IRSA [2]}.
In this section, the representation of IRSA decoding as a bipartite graph is discussed first.
Then the graph perspective distributions are defined, the failure probabilities are derived, and finally, the asymptotic throughput of IRSA is characterized.
It is assumed that users perform path loss inversion-based power control.
We note that a closed form expression for the throughput cannot be derived even for the most basic variant of IRSA due to the underlying graph structure [2]}. Hence, we need to resort to DE, which provides an iterative recipe to compute the throughput.
